Finite Group Databasebeta

← #25007120

Subgroups — #25007120

Order 11008.

420 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 71 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19140288C211yesmaximal, characteristic
2#19134332C211yesmaximal, characteristic
3#19132928C211yesmaximal, characteristic
4#19132623C211yesmaximal, characteristic, complemented
5#19132621C211yesmaximal, characteristic, complemented
6#19132601C211yesmaximal, characteristic, complemented
7C43×#1346C211yesmaximal, characteristic, complemented
8C2×M16×D43—21no—
9C2×#13063316C411yescharacteristic
10C2×#13063283C2211yescharacteristic
11#14582953—21no—
12#14582838C2211yescharacteristic
13#14582836C411yescharacteristic
14#14582825C411yescharacteristic
15#14582798—21no—
16#14582791—21no—
17#14582782—21no—
18#14582770—21no—
19#14582744C411yescharacteristic
20#14582668C2211yescharacteristic
21#14582667—21no—
22#14582625C2211yescharacteristic
23#14582622—21no—
24C43×#398C2211yescharacteristic
25C43×#343C2211yescharacteristic
26C43×#324C2211yescharacteristic
27C22×C4×D43D411yescharacteristic
28C2×#10621877—21no—
29C2×#10621872—41no—
30M16×D43—24no—
31M16×D43—42no—
32C2×C8×D43—41no—
33#13063316—41no—
34#13063316—41no—
35#13063283—41no—
36#13063283—41no—
37C2×C4⋊Dic43—21no—
38C2×C4⋊Dic43—21no—
39C2×C4⋊Dic43C2×C411yescharacteristic
40C2×C4⋊Dic43D411yescharacteristic
41C2×Dic43⋊C4—21no—
42C2×(C2×D43)⋊C4—21no—
43C2×(C2×D43)⋊C4—21no—
44C2×(C2×D43)⋊C4C2×C411yescharacteristic
45C2×(C2×D43)⋊C4D411yescharacteristic
46C2×C4×Dic43—21no—
47C2×C4×Dic43C2×C411yescharacteristic
48C2×C4×Dic43D411yescharacteristic
49Dic43⋊C8—41no—
50C22⋊(C43⋊C8)—21no—
51#13063235—41no—
52C43⋊#95—21no—
53C43⋊#95—21no—
54C43⋊#95—21no—
55C43⋊#95—21no—
56C43⋊#95C2×C411yescharacteristic
57C2×M16×C43—21no—
58C2×C4⋊C4×C43—21no—
59C2×C4⋊C4×C43C2×C411yescharacteristic
60C2×C4⋊C4×C43C2311yescharacteristic
61C22⋊C8×C43—21no—
62#95×C43—21no—
63#95×C43C2×C411yescharacteristic
64C23×D43C22⋊C411yescharacteristic
65C22×C4×C43—21no—
66C22×C4×C43—21no—
67C22×C4×C43C22×C411yescharacteristic
68C22×C4×C43C2×D411yescharacteristic
69C22×C4×C43C2×D411yescharacteristic
70C22×Dic43—21no—
71C22×Dic43—21no—
72C22×Dic43C22⋊C411yescharacteristic
73C22×Dic43C22⋊C411yescharacteristic
74C22×Dic43C22⋊C411yescharacteristic
75C2×C4×D43—21no—
76C2×C4×D43—21no—
77C2×C4×D43—21no—
78C2×C4×D43—21no—
79C2×C4×D43—22no—
80M16×C43—22no—
81M16×C43—41no—
82C2×C8×C43—41no—
83C2×C8×C43—41no—
84C4⋊C4×C43—41no—
85C4⋊C4×C43—41no—
86C4⋊C4×C43—41no—
87C4⋊C4×C43—41no—
88(C2×D43)⋊C4—41no—
89(C2×D43)⋊C4—41no—
90(C2×D43)⋊C4—42no—
91(C2×D43)⋊C4—42no—
92C4⋊Dic43—41no—
93C4⋊Dic43—42no—
94C4⋊Dic43—42no—
95C4⋊Dic43—41no—
96Dic43⋊C4—41no—
97Dic43⋊C4—41no—
98C4×Dic43—21no—
99C4×Dic43—21no—
100C4×Dic43—21no—
101C4×Dic43—21no—
102C4×Dic43—42no—
103#10621877—22no—
104#10621877—41no—
105C2×C43⋊C8—41no—
106C2×C43⋊C8—41no—
107#10621872—44no—
108C8×D43—44no—
109C23×C43C2×C22⋊C411yescharacteristic
110C22×D43—21no—
111C22×D43—21no—
112C22×D43—41no—
113C22×D43—41no—
114C22×D43#10412yes—
115C2×C4×C43—21no—
116C2×C4×C43—21no—
117C2×C4×C43—22no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—41no—
121C2×C4×C43—41no—
122C2×C4×C43—41no—
123C2×C4×C43—41no—
124C2×C4×C43—41no—
125C2×C4×C43—41no—
126C2×C4×C43—41no—
127C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
128C2×C4×C43#13711yescharacteristic
129C2×Dic43—21no—
130C2×Dic43—21no—
131C2×Dic43—21no—
132C2×Dic43—21no—
133C2×Dic43—41no—
134C2×Dic43—41no—
135C2×Dic43—41no—
136C2×Dic43—41no—
137C2×Dic43—41no—
138C2×Dic43—41no—
139C2×Dic43—41no—
140C2×Dic43—41no—
141C2×Dic43#9911yescharacteristic
142C2×Dic43#9911yescharacteristic
143C4×D43—22no—
144C4×D43—22no—
145C4×D43—22no—
146C4×D43—22no—
147C8×C43—42no—
148C8×C43—81no—
149C43⋊C8—42no—
150C43⋊C8—81no—
151#11767—431nomaximal, Sylow
152C22×C43—21no—
153C22×C43—21no—
154C22×C43C2×#9911yescharacteristic
155C22×C43#41711yescharacteristic
156C22×C43C2×#10411yescharacteristic
157C2×D43—22no—
158C2×D43—41no—
159C2×D43—41no—
160C2×D43—42no—
161C2×D43—81no—
162C4×C43—21no—
163C4×C43—21no—
164C4×C43—42no—
165C4×C43—41no—
166C4×C43—41no—
167C4×C43—81no—
168Dic43—21no—
169Dic43—21no—
170Dic43—41no—
171Dic43—41no—
172Dic43—81no—
173Dic43—81no—
174#2611—431no—
175#1742—431no—
176#1464—431no—
177#1353—431no—
178#1353—431no—
179#1346—431no—
180#1346D4311yescharacteristic, complemented
181C2×C43—21no—
182C2×C43—21no—
183C2×C43#150411yescharacteristic
184C2×C43#212311yescharacteristic
185C2×C43#213211yescharacteristic
186D43—42no—
187C22×M16—861no—
188C2×#125—431no—
189C2×#117—431no—
190#432—861no—
191#400—431no—
192#399—431no—
193#398C2×D4311yescharacteristic
194#397—431no—
195#389—861no—
196#388—861no—
197#387—861no—
198#385—861no—
199#376—431no—
200#343—431no—
201#343—861no—
202#343C2×D4311yescharacteristic
203#324—431no—
204#324C2×D4311yescharacteristic
205#323—861no—
206C43#1176711yescharacteristic, complemented, Sylow
207C23×C4—431no—
208C2×M16—21no—
209C2×M16—864no—
210C2×M16—861no—
211C2×M16—1721no—
212C2×M16—1722no—
213C22×C8—1721no—
214#125—1721no—
215#125—1721no—
216#117—1721no—
217#117—1721no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—431no—
220C2×C4⋊C4—431no—
221C2×C4⋊C4—861no—
222C2×C4⋊C4—861no—
223C2×C4⋊C4—861no—
224C2×C4⋊C4C4×D4311yescharacteristic
225C2×C4⋊C4C22×D4311yescharacteristic
226C2×C22⋊C4—431no—
227C2×C22⋊C4—431no—
228C2×C22⋊C4—861no—
229C2×C22⋊C4—861no—
230C2×C42—431no—
231C2×C42—431no—
232C2×C42—861no—
233C4⋊C8—1721no—
234C22⋊C8—21no—
235C22⋊C8—861no—
236#97—1721no—
237#95—21no—
238#95—431no—
239#95—861no—
240#95—861no—
241#95—861no—
242#95—861no—
243#95C4×D4311yescharacteristic
244C24—431no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—431no—
248C22×C4—431no—
249C22×C4—431no—
250C22×C4—861no—
251C22×C4—861no—
252C22×C4—862no—
253C22×C4—861no—
254C22×C4—861no—
255C22×C4—861no—
256C22×C4—861no—
257C22×C4C2×C4×D4311yescharacteristic
258C22×C4D4×D4311yescharacteristic
259C22×C4D4×D4311yescharacteristic
260M16—22no—
261M16—41no—
262M16—862no—
263M16—1724no—
264M16—1721no—
265C2×C8—41no—
266C2×C8—41no—
267C2×C8—1724no—
268C2×C8—1721no—
269C2×C8—1721no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—1721no—
275C4⋊C4—1721no—
276C4⋊C4—1722no—
277C4⋊C4—1721no—
278C4⋊C4—1721no—
279C4⋊C4—1722no—
280C22⋊C4—1721no—
281C22⋊C4—1721no—
282C22⋊C4—1722no—
283C22⋊C4—1722no—
284C42—861no—
285C42—861no—
286C42—861no—
287C42—861no—
288C42—1722no—
289C23—432no—
290C23—861no—
291C23—861no—
292C23—1721no—
293C23—1721no—
294C23C22⋊C4×D4311yescharacteristic
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—22no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—431no—
308C2×C4—431no—
309C2×C4—862no—
310C2×C4—862no—
311C2×C4—862no—
312C2×C4—862no—
313C2×C4—861no—
314C2×C4—861no—
315C2×C4—861no—
316C2×C4—861no—
317C2×C4—1721no—
318C2×C4—1721no—
319C2×C4—1721no—
320C2×C4—1721no—
321C2×C4—1721no—
322C2×C4—1721no—
323C2×C4—1721no—
324C2×C4—1721no—
325C2×C4#1306334911yescharacteristic
326C2×C4#1306335411yescharacteristic
327C8—42no—
328C8—81no—
329C8—3441no—
330C8—1722no—
331C22—21no—
332C22—21no—
333C22—862no—
334C22—3441no—
335C22—1722no—
336C22—1721no—
337C22—1721no—
338C22#99×D4311yescharacteristic
339C22#1458289711yescharacteristic
340C22#104×D4311yescharacteristic
341C4—21no—
342C4—21no—
343C4—42no—
344C4—41no—
345C4—41no—
346C4—81no—
347C4—861no—
348C4—861no—
349C4—3441no—
350C4—3441no—
351C4—1721no—
352C4—1721no—
353C2—21no—
354C2—21no—
355C2—1722no—
356C2#1913309611yescharacteristic
357C2#1913624711yescharacteristic
358C2#1913627911yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1346C2
socleC22×C43C2×#99
prime radicalC23×D43C22⋊C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1346D43
hypocenterC43#11767
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1346

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
4. #19132623C2semidirect
5. #19132621C2semidirect
6. #19132601C2semidirect
7. C43×#1346C2semidirect
180. #1346D43semidirect
206. C43#11767semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#191402882
#191343322
#191329282
#191326232
#191326212
#191326012
C43×#13462
#1176743